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1 and 2 for polyelectrolyte concentrations greater than the entanglement concentration ce . D. Unresolved Issues Although the theory of polyelectrolyte dynamics reviewed here provides approximate crossover formulas for the experimentally measured diffusion coefficients, electrophoretic mobility, and viscosity, the validity of the formulas remains to be established. In spite of the success of one unifying conceptual framework to provide valid asymptotic results, in qualitative agreement with experimental facts, it is desirable to establish quantitative validity.

Similarly, the electrophoretic mobility follows from the formula m $ QD as m $ N 1Àd ð319Þ so that m $ N À2 if entropic barriers dominate and m $ N À1 if reptation limit is approached. There has been substantial experimental support for the presence of entropic barrier mechanism for polymer dynamics [65, 66]. Recently, there have been several electrophysiology experiments [67–71], where translocation of 52 m. muthukumar single polyelectrolyte molecules through protein channels is investigated. Under the conditions of these experiments, the entropic barrier mechanism is the dominant polymer dynamics [72–76].

278)–(281) show that m is independent of N: ( 0 0 kRg ( 1 c N ; ð322Þ m $ N0 pﬃﬃ ; kRg ) 1 c In addition, we predict that m is independent of polyelectrolyte concentration c at low salt concentrations and decreases with c as the salt concentration is polyelectrolyte dynamics 53 increased. There is also an additional salt concentration dependence of m as shown in Eq. (281). It is to be remarked that in the Rouse regime, the Hu¨ ckel law of electrophoretic mobility is valid, m¼ QD kB T ð323Þ whereas in dilute solutions this law is significantly modified, m¼ QD MðkRg Þ kB T ð324Þ where MðkRg Þ is defined in Eq.